Being a stay at home parent is like a job but you don't get paid for it. It's like volunteer work. It also has a lot of similarities to other jobs that require to care for someone else. Ex. Child day care who care for multiple children at once. :)
By the exact definition of the word, A job is "a paid position of regular employment" emphasis on the word paid. So technically a stay at home parent is not like a job, Although it is very important and sometimes necessary to do with a child, It is not a job.